Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture
There were carried out modeling of radiolysis processes in the water–hexane system for the purpose of to identify the mechanism of radiolysis and comparison of theoretical and experimental data. Проведено математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан с целью выяв...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2013
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| Zitieren: | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture / T.N. Agayev // Вопросы атомной науки и техники. — 2013. — № 5. — С. 43-47. — Бібліогр.: 11 назв. — англ. |
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| author_facet | Agayev, T.N. |
| citation_txt | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture / T.N. Agayev // Вопросы атомной науки и техники. — 2013. — № 5. — С. 43-47. — Бібліогр.: 11 назв. — англ. |
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| description | There were carried out modeling of radiolysis processes in the water–hexane system for the purpose of to identify the mechanism of radiolysis and comparison of theoretical and experimental data.
Проведено математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан с целью выявления механизма радиолиза и сравнение теоретических данных с экспериментальными.
Проведено математичне моделювання процесів радіолізу, води, гексану та суміші вода–гексан з метою виявлення механізму радіолізу та порівняння теоретичних даних з експериментальними.
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ISSN 1562-6016. ВАНТ. 2013. №5(87) 43
UDС 541.15
MATHEMATICAL MODELING OF PROCESSES OF RADIOLYSIS OF
WATER, HEXANE AND WATER–HEXANE MIXTURE
T.N. Agayev
Institute of Radiation of Azerbaijan National Academy of sciences, Baku, Azerbaijan
E-mail: agayevteymur@rambler.ru
There were carried out modeling of radiolysis processes in the water–hexane system for the purpose of to
identify the mechanism of radiolysis and comparison of theoretical and experimental data.
INTRODUCTION
In identifying the mechanism of radiation-chemical
processes modeling and determination of kinetic
parameters are of particular importance. Comparison of
experimental and calculated values of the parameters of
the radiation-chemical processes makes it possible to
judge the reliability of the proposed mechanism.
Therefore based on the known literature data about
the mechanism and model calculations of the radiation-
chemical processes in water and hydrocarbon systems
there were simulated radiolysis processes in hexane and
hexane-water system by us [1, 2].
In order to explain the obtianed experimental data
and reveal possible mechanisms of the reactions upon
radiolysis of water, hexane and ware-hexane mixture
modeling of the processes occuring in these systems has
been carried out. In this modeling the following factors
were taken into account: dose rate, volume of the
irradiated system, time of irradiation, concentartions of
components, constants of the reactions rates, etc.
Modeling of the process kinetics has been made wich
computer program GEPASI 3 for the Windows
operating system. Description of this program is given
in [3, 4]. Constants of the reactions rates are taken from
[5, 11].
The main purpose of the modeling is to study the
processes occuring in the water – hexane mixture upon
γ-raiolysis. However, for comparison with the
literature, separate radiolysis separately of liquid water
and hexane was first modeled. In the case of liquid
water rate constants from [5, 9, 11] as well as our own
experimental data were used:
Dose rate – 1,42 Gy/s.
Volume of ampoules – 0,5 ml.
Time of irradiation – from 1 to 20 hr.
The reactions and rate constants of the reactions
taken from [5] are given below:
Table 1
Namber of
reaction Reaction К1-constant of direct
reaction, l/mole·s
К2-constant of direct
reaction, l/mole·s
1 2еaq + 2Н2О→H2 + 2OH- 4,97·109
2 еaq + H + Н2О→H2 + OH- 1,89·1010
3 еaq + OH→ OH- 3·1010
4 еaq + О + Н2О →2 OH- 2,2·1010
5 еaq + НО2→ НО2
- 2·1010
6 еaq + O2
- + Н2О→ OH- + НО2
- 1,3·1010
7 еaq + Н2О2→ OH- + ОН 1,2·1010
8 еaq + НО2
-→ OH- + О- 3,5·109
9 еaq + О2→ О2
- 1,8·1010
10 еaq + Н+→Н 2,3·1010
11 еaq + Н2О→ OH- + Н 19
12 2Н→Н2 7,8·109
13 Н + ОН→ Н2О 2,5·1010
14 Н + НО2→ Н2О2 2·1010
15 Н + О2
-→ НО2
- 2·1010
16 Н2О2 + Н→ ОН + Н2О 8,42·106
17 О2 + Н→ НО2 2,1·1010
18 OH- + Н→ Н2О- 2,2·107
19 2 ОН↔ Н2О2 5,5·109 1,33·10-7
20 ОН + О-→ НО2
- 2·1010
21 ОН + НО2→ О2 + Н2О 6,3·109
22 ОН + О2
-→ О2 + OH- 8,2·109
23 Н2О2 + ОН→ НО2 + Н2О 4,06·107
24 ОН + НО2
-→ OH- + НО2 7,5·107
25 Н2 + ОН→ Н + Н2О 3,8·107
26 OH-+ OH↔ О- + Н2О 1,2·1010 1,75·106
44 ISSN 1562-6016. ВАНТ. 2013. №5(87)
27 2 О- + Н2О→ OH- + НО2
- 1·109
28 О2
- + О- + Н2О→ О2 + 2 OH- 6·108
29 Н2О2 + О-→ О2
- + Н2О 5·108
30 О- + НО2
-→ OH- + О2
- 4·108
31 Н2 + О-→ OH- + Н 8·107
32 2 НО2→ Н2О2 + О2 8,3·105
33 НО2 + Н2О2→ О2 + OH + Н2О 0,2
34 О2
- + НО2→ О2 + НО2
- 9,7·107
35 НО2↔H+ + О2
- 7,5·105 5,1·1010
36 2 О2
- + 2Н2О→ Н2О2 + О2 + 2 OH- 0,3
37 Н2О2 + О2
-→ О2 + OH- + OH 0,13
38 О2
- + НО2
-→ О2 + OH- + О- 0,13
39 Н2О2 + OH- ↔НО2
- + Н2О 1·1010 1,13·106
40 H+ + НО2
-→ Н2О2 2·1010
41 H+ + OH-↔ Н2О 1,4·1011 2,52·10-5
42 О2 + О-↔О3
- 3·109 300
43 О- + О3
-→2 О2
- 7·109
44 Н2О2 + О3
-→ О2 + О2
- + Н2О 1,6·106
45 НО2
- + О3
-→ О2 + OH- + О2
- 8,9·105
46 Н2 + О3
-→ О2 + OH- + Н 2,5·105
47 H+ + О-→ OH 1·1010
48 OH- + НО2→ О2
- + Н2О 1·1010
In the modeling the values of the particles yielde
given in [5] werw also used:
Table 2
Particle G, particles/100 eV
Н2О- 2,7
Н 0,6
Н2 0,45
ОН 2,7
Н2О2 0,7
О2- 0,02
Н+ 3,42
ОН- 0,7
еaq 2,7
Based on these data we have built several graphs and
then carried out their comparison with the graphs given
in literature,in particular, in [5, 6].
Sufficient coincidence is observed which may serve
as an evidence of correctness of the selected scheme and
the used program.In the case of hexane the rate
constants of the reactions from [6–8, 10] wereused and
the experimental data remained as in the case of liquid
water.
The reactions and the rate constants of the reactions
taken from [6, 7] and [9] are given belo.
Table 3
Namber of
reaction Reaction К1-constant of direct reaction, l/mole·s
1 C6H14
+ + e→ C6H14
* 3·109
2 C6H14
*→C6H13
• + H 8·10-4
3 C6H14
*→C6H12 + H2 4·10-4
4 C6H14 + H→ C6H13
• + H2 1,5·108
5 C6H13
• + C6H13
•→ C6H12 + C6H14 1·1010
6 C6H14
*→CH3
• + C5H11
• 2,7·10-5
7 C6H14
*→C2H5
• + C4H9
• 4·10-6
8 C6H14
*→C3H7
• + C3H7
• 6·10-3
9 C2H5
• + C2H5
•→C4H10 1·1010
10 C3H7
• + C3H7
•→C3H8 + C3H6 1·1010
11 C2H6 + H→ C2H5
• + H2 3·104
12 CH4 + H→ CH3
• + H2 1·104
13 C3H8 + H→ C3H7
• + H2 4,5·104
14 C4H10 + H→ C4H9
• + H2 6,21·104
15 C5H12 + H→ C5H11
• + H2 9,1·104
16 CH3
• + CH3
•→ C2H6 1·1010
17 CH3
• + H→ CH4 2,3·109
18 C2H5
• + H→ C2H6 3·109
19 C3H7
• + H→ C3H8 8·109
20 C4H9
• + H→ C4H10 5,2·109
21 C5H11
• + H→ C5H12 5·109
ISSN 1562-6016. ВАНТ. 2013. №5(87) 45
22 C6H13
• + H→ C6H14 5,5·109
23 CH3
+ + CH4→ C2H5
+ + H2 6·1011
24 CH4
+ + CH4→ CH5
+ + CH3
• 7,6·1011
25 C2H4
+ + C2H4→ C4H8
+ 1,2·1011
26 C2H4
+ + C2H4→C4H7
+ + H 9·1010
27 C2H6 + C2H6
+→ C4H10
+ + H2 2,4·109
28 C2H6 + C2H6
+→ C4H9
+ + H2 +H 6·109
In the modelling the values of the particles yieds
given in [6] were also used:
Table 4
Based on these data we have built kinetic curves for
H2, CH4, ΣC2=[C2H6]+[C2H4], ΣC3=[C3H8]+[C3H6],
ΣC4=[C4H10]+[C4H8] and ΣC5=[C5H12]. In these graphs,
along the ordinate axis the amount of molecules of a
given substance is set while along the abscissa axis time
in hours is shown (Fig. 1−4).
According to these curves the rates of accumulation
of radiolysis products and their radiation-chemical
yields were calculated. The results also coincide with
the data given in literature, for example, in [6].
Bellow, the values of particle accumulation rate W
and yield G are given which were obtained upon
radiolysis of hexane at the dose rate of 1,42 Gy/s.
Fig.1. Kinetics of molecular hydrogen accumulation
upon radiolysis of hexane at T=300 K and dose rate
of 1,42 Gy/s
Fig. 2. Kinetics of methane accumulation upon
radiolysis of hexane at T=300 K and dose rate of
1,42 Gy/s
Fig. 3. Kinetics of ethane, propane and butane
accumulation upon radiolysis of hexane at T=300 K
and dose rate of 1,42 Gy/s
Fig. 4. Kinetics of pentane accumulation upon
radiolysis of hexane at T=300 K and dose rate
of 1,42 Gy/s
Particle G, particles/100 eV
СН3 0,7
С2Н5 0,3
С3Н7 0,3
С4Н9 0,27
С6Н13 4,1
е 0,12
Н2 5
СН4 0,18
С2Н6 0,42
С3Н8 0,41
С3Н6 0,19
С4Н10 0,35
С5Н12 0,1
С6Н12 0,86
С2Н4 0,25
С4Н8 0,14
С6Н14
+ 0,12
46 ISSN 1562-6016. ВАНТ. 2013. №5(87)
Modeling of radiolysis of water – hexane mixture
has been carried out taking into consideration slight
solubility of water in hexane and vice versa. For this
reason it was assumed that radiolysis of this system is
similar to the radiolysis of each of the components in
seperate. However, taking into account possibility of
diffusion of the radiolysis primary products from one
phase into another, several new reactions with the
respective rate constants [10] were added to the above-
indicated reactions:
Table 5
Modeling was performed for the mixture of the
following percentage content of the components:
50 % С6Н14 + 50 % Н2О, which in the experiment
corresponded to the following volume ratio of the
components: 0,2 ml С6Н14 + 0,2 ml Н2О. The kinetic
curves were built for H2, CH4, ΣC2 = [C2H6]+[C2H4],
ΣC3 = [C3H8]+[C3H6], ΣC4 = [C4H10]+[C4H8] and
ΣC5 = [C5H12], where along the ordinate axis the number
of molecules of a given substance and along the
abscissa axis time in hours have been set. Our
experimental data are shown as dotted curves in these
graphs (Fig. 5–9):
Fig. 5. Kinetics of molecular hydrogen accumulation
upon radiolysis of the water-hexane mixture at dose rate
of 0,9 Gy/s and of various ratios of the components:
1 – С6Н14/ Н2О=0,05 ml/0,45 ml;
2 – С6Н14/ Н2О=0,15 ml/0,35 ml;
3 – С6Н14/ Н2О=0,25 ml/0,25 ml
Fig. 6. Kinetics of methane accumulation upon
radiolysis of water-hexane mixture at T=300 K
and dose rate of 0,9 Gy/s
Fig. 7. Kinetics of ethane and propane accumulation
upon radiolysis of water-hexane mixture at T=300 K
and dose rate of 0,9 Gy/s
Fig. 8. Kinetics of butane accumulation upon radiolysis
of water - hexane mixture at T=300 K and dose rate of
0,9 Gy/s
Fig. 9. Kinetics of pentane accumulation upon
radiolysis of waterhexane mixture at T=300 K
and dose rate of 0,9 Gy/s
Products of radiolysis Н2 СН4 С2Н6 С3Н8 С4Н10 С5Н12
W (×10-14), molecules/s 3 0,12 0,56 0,57 0,3 0,06
G, molecules/100 eV 3,4 0,14 0,6 0,6 0,34 0,07
ISSN 1562-6016. ВАНТ. 2013. №5(87) 47
Based on these values of rates of particle
accumlation W and their yield G have been calculated.
The obtained data were compared with the experimental
data at the same volume ratio of components, which
correspond to dotted lines.
The comparison shows quite a good coincidence of
the results that may serve as an evidence of correctness
of the assumptions made. The results of modeling of
radiolysis of the mixture С6Н14 + Н2О dose rate of
0,9 Gy/s is given bellow:
Table 6
Products of
radiolysis СН4 С2Н6 С3Н8 С4Н10 С5Н12
W (×10-14),
molecules/s 0,7 1,12 1,12 0,56 0,14
G, molecu-
es/100 eV 0,13 0,2 0,2 0,1 0,025
Modeling was separately made for kinetics of
hydrogen formation upon radiolysis of С6Н14 + Н2О
mixture of the above-shown percentage ratio of the
components at dose rate of 1,42 Gy/s:
Products of radiolysis .......................... Н2
W (×10-14), molecules/s....................... 2,8
G, molecules/100 eV ........................... 3,3
All of the afore-cited reaction rate constants
obtained from data about the stationary radiolysis, and
there were taken into an account the presence of a gas
volume over the irradiated liquid. Although the
radiolysis occurring in the gas phase at room
temperature can almost always be neglected, but such
products of radiolysis of water as hydrogen and oxygen,
depending on the experimental conditions are
distributed differently between the phases. In addition,
in the presence of initially dissolved hydrogen some
reactions may have a chain character and the beginning
of the chain is atoms of hydrogen. So, without proper
taking into account of this circumstance the final result
of radiolysis is quantitatively unpredictable. However, if
the irradiated volume is constantly shaking, the
distribution of radiolysis gas between the phases
become to equilibrium. All these requirements were
taken into account when selecting certain constants
from different sources.
Thus, the simulation data of water radiolysis
coincide with the published data, which confirms the
loyalty of chosen methodology. But model data of the
radiolysis of hexane and hexane-water mixture
coincided with the experimental data within the
accuracy of the determination of the rate constant of
used reactions.
REFERENCES
1. A.A. Garibov, K.T. Eyubov, T.N. Agayev.
Liquid-phase radiolysis of water-n-hexane system //
Ch.H.E. 2004, v. 38, №5, p. 334-336.
2. A.A. Garibov, K.T. Eyubov, T.N. Agayev. The
hydrogen generation during water hexane system
radiolysis // Journal of Turkish atomic energy authority
(TAEK). 2003, №2, p. 48-50.
3. P. Mendes. GEPASI: A Software Package for
modeling the Dynamics, steady States and Control of
Biochemical and Other Systems // Comput. Applic.
Biosci. 1993, v. 9, p. 563-571.
4. P. Mendes. Biochemistry by Numbers:
Simulation of Biochemical Pathways with GEPASI 3.
// Trends Biochem. Sci. 1997, v. 22, p. 361-363.
5. V. Bugayenko, V. Byakov. Quantitative Model
of Radiolysis of liquid Water and Diluted Aqueouns
Solutions of Hydrogen, Oxygen and Hydrogen Peroxide.
I. Model Formulation: Preprints of Institute of
Theoretical and Experimental Physics. 1991, №74, 24 p.
6. A. Pikaev. Modern Radiation Chemistry.
Radiolysis of Gases and liquids. Moscow: “Nauka”,
1986, p. 440.
7. V. Kondratyev. Rate Constants of gas-Phase
Reactions. M.: “Nauka”, 1970, 351 p.
8. V. Zhdanov. Rate of Chemical Reaction.
Novosbirsk: “Nauka”, 1986, 100 p.
9. A. Pikaev, S. Kabakchi. Reactivity of Primary
Products of Water Radiolysis. M.: “Energoatomizdat”,
1982, 199 p.
10. Ed. Palm V. Tables of Rate Constants and
Equilibrium of Heterolytic Organic Compounds. M.:
VINITI, 1975, 431 p.
11. E. Denisov. Rate Constants of Homolytic Liquid-
Phase Reactions. M.: “Nauka”, 1971, 711 p.
Статья поступила в редакцию 12.07.2012 г.
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ РАДИОЛИЗА ВОДЫ,
ГЕКСАНА И СМЕСИ ВОДА–ГЕКСАН
Т.Н. Агаев
Проведено математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан с
целью выявления механизма радиолиза и сравнение теоретических данных с экспериментальными.
МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ПРОЦЕСІВ РАДІОЛІЗУ ВОДИ, ГЕКСАНУ
ТА СУМІШІ ВОДА–ГЕКСАН
Т.Н. Агаєв
Проведено математичне моделювання процесів радіолізу, води, гексану та суміші вода–гексан з метою
виявлення механізму радіолізу та порівняння теоретичних даних з експериментальними.
|
| id | nasplib_isofts_kiev_ua-123456789-111416 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:56:23Z |
| publishDate | 2013 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Agayev, T.N. 2017-01-09T19:45:03Z 2017-01-09T19:45:03Z 2013 Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture / T.N. Agayev // Вопросы атомной науки и техники. — 2013. — № 5. — С. 43-47. — Бібліогр.: 11 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111416 541.15 There were carried out modeling of radiolysis processes in the water–hexane system for the purpose of to identify the mechanism of radiolysis and comparison of theoretical and experimental data. Проведено математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан с целью выявления механизма радиолиза и сравнение теоретических данных с экспериментальными. Проведено математичне моделювання процесів радіолізу, води, гексану та суміші вода–гексан з метою виявлення механізму радіолізу та порівняння теоретичних даних з експериментальними. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Физика радиационных повреждений и явлений в твердых телах Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture Математичне моделювання процесів радіолізу води, гексану та суміші вода–гексан Математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан Article published earlier |
| spellingShingle | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture Agayev, T.N. Физика радиационных повреждений и явлений в твердых телах |
| title | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| title_alt | Математичне моделювання процесів радіолізу води, гексану та суміші вода–гексан Математическое моделирование процессов радиолиза воды, гексана и смеси вода–гексан |
| title_full | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| title_fullStr | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| title_full_unstemmed | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| title_short | Mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| title_sort | mathematical modeling of processes of radiolysis of water, hexane and water–hexane mixture |
| topic | Физика радиационных повреждений и явлений в твердых телах |
| topic_facet | Физика радиационных повреждений и явлений в твердых телах |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111416 |
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